<i>SU</i>(3)×𝒮<sub>20</sub> algebras for uniform spin‐1 ensembles on [<sup>2</sup><i>H</i><sup>12</sup><i>C</i>]<sub>20</sub>, or [<sup>14</sup><i>N</i>]<sub>20</sub>, dodecahedrane‐type lattices and analogous isotopomeric [<i>M</i><sub>20</sub><sup>12</sup><i>C</i><sub>40</sub>] met‐carb subensembles: <i>M</i>‐based cardinalities and completeness of 𝒮<sub>20</sub> spin irreps, via hierarchical {𝒞<sup>λ⊢(<i>n</i>=20):(<i>M</i>)</sup>} designs of polyhedral combinatorics*
Bibliographic record
Abstract
Abstract The M‐based hierarchy cardinalities of spin irreps for \documentclass{article}\pagestyle{empty}\begin{document}$[A]_{20}^{(I_{i}=1)}$\end{document} uniform nuclear magnetic resonance (NMR) /isotopomer spin ensembles are derived. Such ideas define the completeness of the number‐partition‐based (intermediate) combinatorial designs (on M) themselves inherent in specific λ⊢n digit assembly combinatorial properties. Illustrative M‐subspatial irrep subsets are derived via Schur decompositions from symbolic algorithms (Sagan, B. E. Symmetric Group: Representations, C‐Algorithms, Symmetric Functions; Wadsworth: Belmont, CA, 1991; SYMMETRICA package, as per Kerber, A.; Kohnert, A.; Lascoux, A. Symbolic Comput 1992, 14, 195). The results are discussed in the context of the independant cardinality of underlying system scalar invariants (SI) corresponding to the democratic auxiliary labels (Chem Phys 1998, 238, 245; J Math Chem in press), or projective recoupling, of 20‐fold dual tensorial sets. Landau‐like 𝒮n‐maps for fundamental terms plus statistical weighted subsidary maps yield the independent ∣SI∣s (see Europhys Lett in press). Geometric aspects of the dual group mappings imply that eventually large cage NMR ensembles must be governed by a local, rather than a global, symmetry, with the former related to established spectral deceptive NMR. This suggests a further role for dynamical networks in NMR, beyond that given by K. Balasubramanian (J Chem Phys 1983, 78, 6369) as implied by D. Watts (Small Worlds; Princeton Univ. Press: Princeton, NJ, 1999). © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.006 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".